Method and system for statistical filters and design of statistical filters

Abstract

Systems and methods for the design or implementation of statistical filters for use in the spectral shaping of transmissions are disclosed. A desired power spectrum may be mapped to find pole locations that approximate the desired spectrum. These pole locations may then be mapped to the edge or inside of an equilateral polygon lying inside a unit circle, the equilateral polygon having the same number of sides as the order of the statistical filter desired and one vertex mapped to unity, to yield a set of eigenvalues. These eigenvalues may be the eigenvalues of a stochastic matrix the elements of which may be the Markov transition probabilities for use in a statistical filter designed to achieve the desired power spectrum. Use of a statistical filter employing these Markov transition values may be utilized to shape UWB or other signals to achieve the desired power spectrum.

Description

CROSS-REFERENCE TO RELATED APPLICATION[0001]This application is a continuation of, and claims a benefit of priority under 35 U.S.C. 120 of the filing date of U.S. patent application Ser. No. 11 / 218,335 by inventors James L. Lansford and Shyam Sunder Uma Chander, entitled “Method and System for Statistical Filters and Design of Statistical Filters” filed on Sep. 1, 2005 now U.S. Pat. No. 7,184,938, which in turn claims the benefit of priority under 35 U.S.C. § 119 to provisional patent application No. 60 / 606,479 filed Sep. 1, 2004, the entire contents of which are hereby expressly incorporated by reference for all purposes.RELATED APPLICATIONS[0002]This application claims a benefit of priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 60 / 606,479 by inventors Jim Lansford and Shyam Sunder Uma Chander entitled “System and Method For Pulse Shape Filtering” filed on Sep. 1, 2004, the entire contents of which are hereby expressly incorporated by reference for all...

AI Technical Summary

Benefits of technology

[0018]Aspects of the invention will provide the technical advantage of allowing the resolution of a wide variety of interference issues between devices which utilize overlapping portions of the same spectrum. More specifically, the present invention will allow the implementation of filters which allow a significant amount of spectrum shaping with less data or signal distortion than previous spectrum shaping techniques. Furthermore, the present invention allows the design and implementation of filters which can provide spectrum shaping for a wide variety of transmission methodologies and which can be designed and implemented based on a desired power spectrum.

Problems solved by technology

For example, transferring a 1 Gbyte file full of vacation pictures from a digital camera to a computer take merely seconds with UWB compared to hours using other currently available, technologies (i.e. Bluetooth) and consume far less battery power in doing so.

Consequently, if a UWB device was in close proximity to another wireless system there is a significant potential for interference between the UWB device and the wireless system.

Thus, there is a potential for UWB systems to interfere with television reception of those types of system.

These types of digital notch filters, however, are highly problematic in real-world applications as they tend to be highly disruptive, distorting the pulse shape of a transmitted UWB signal, introducing ringing and interchip interference and hence destroying information contained in the pulse shape while making the signal harder to decode.

These types of disruptions occur mainly because of spectral loss and time dispersion side effects of the finite impulse response filters.

In addition, certain types of these pulse shaping filters may add cost and complexity.

Unfortunately, due to the mathematical complexity of statistical filter, equation based design of these filters is difficult.

More specifically, traditionally it has been difficult to design a statistical filter to meet the specification of a given power spectrum.

While various sorts of line coding techniques have been experimented with, no systematic method has been demonstrated in the literature that can shape a line code to fit an arbitrary spectral shape.

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